Geodesic
Hyperidentities in many-sorted algebras
Discussiones Mathematicae. General Algebra and Applications, Tome 29 (2009) no. 1, pp. 47-74

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The theory of hyperidentities generalizes the equational theory of universal algebras and is applicable in several fields of science, especially in computers sciences (see e.g. [2,1]). The main tool to study hyperidentities is the concept of a hypersubstitution. Hypersubstitutions of many-sorted algebras were studied in [3]. On the basis of hypersubstitutions one defines a pair of closure operators which turns out to be a conjugate pair. The theory of conjugate pairs of additive closure operators can be applied to characterize solid varieties, i.e., varieties in which every identity is satisfied as a hyperidentity (see [4]). The aim of this paper is to apply the theory of conjugate pairs of additive closure operators to many-sorted algebras.
Keywords: hypersubstitution, hyperidentity, heterogeneous algebra 
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Denecke, Klaus; Lekkoksung, Somsak. Hyperidentities in many-sorted algebras. Discussiones Mathematicae. General Algebra and Applications, Tome 29 (2009) no. 1, pp. 47-74. http://geodesic.mathdoc.fr/item/DMGAA_2009_29_1_a3/